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If N, C, and D are positive integers, what is the remainder

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If N, C, and D are positive integers, what is the remainder [#permalink] New post 06 Nov 2012, 17:35
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If N, C, and D are positive integers, what is the remainder when D is divided by C?

1) If D+1 is divided by C+1, the remainder is 5.
2) If ND+NC is divided by CN, the remainder is 5.
[Reveal] Spoiler: OA

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Re: If N, C, and D are positive integers, what is the remainder [#permalink] New post 06 Nov 2012, 17:54
1. insufficient b/c D and C can be any number. adding +1 can change remainder completely.
ex: D =2 , C = 3 R = 2 ... D = 2+1 , C = 3+1 R = 3
2: sufficient b/c (ND + NC)/CN => ND/CN + NC/CN => ND/CN =>D/C + 1 => R5

answer: B
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Re: If N, C, and D are positive integers, what is the remainder [#permalink] New post 11 Sep 2013, 03:20
Can someone please help with a detailed explanation? Was able to get the answer right but don't really know how I arrived at it.

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Re: If N, C, and D are positive integers, what is the remainder [#permalink] New post 14 Oct 2014, 12:11
1) insufficient
2) ND+NC/CN gives a remainder of 5.

ND + NC / CN = (D+C)/C

So we know that (D+C)/C gives a remainder of 5.

The idea here is that if you add any multiple of C to C then you will definitely get a multiple of C. For eg. 4 is a multiple of 2. So (4+2)/2 will give R=0.
In this case though we have a number added to C leaving a remainder of 5. This means that D is not divisible by C and that D must leave a remainder of 5. Eg. (5+0)/10 leaves a remainder of 5 . (5+10)/10 will leave a remainder of 5 also. So the remainder will always be in D in the equation (D+C). This means that D/C will also give us a remainder of 5. Sufficient.
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Re: If N, C, and D are positive integers, what is the remainder [#permalink] New post 14 Oct 2014, 22:17
Expert's post
kingb wrote:
If N, C, and D are positive integers, what is the remainder when D is divided by C?

1) If D+1 is divided by C+1, the remainder is 5.
2) If ND+NC is divided by CN, the remainder is 5.


Stmnt 1: If D+1 is divided by C+1, the remainder is 5.

D+1 = (C+1)k + 5
D = Ck + (k + 4)
When D is divided by C, the remainder will vary with k.
If k = 0, remainder will be 4 (C is greater than 4)
If k = 1, remainder will be 5 (C is greater than 5)
If k = 2, remainder will be 6 (C is greater than 6)
etc

2) If ND+NC is divided by CN, the remainder is 5.
ND + NC = CN*k + 5
DN = CN*(k-1) + 5
D = C*(k-1) + 5/N
Now, N is a positive integer and remainder must be a positive integer too. The only value that N can take such that 5/N is a positive integer is 1. So N must be 1.
D = C*(k -1) + 5
When D is divided by C, remainder is 5.

Answer (B)
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Re: If N, C, and D are positive integers, what is the remainder   [#permalink] 14 Oct 2014, 22:17
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